Model-free kinetics

Many other examples could have been selected in the area of solvate investigation. Numerous reports of dehydration kinetic studies on drug hydrates are found in the pharmaceutical literature. An instructive recent case concerns piroxicam monohydrate (PM) [67]. Model-free kinetics showed that the dehydration kinetics of PM under isothermal and non-isothermal conditions were different. Complementary structural studies revealed a complex hydrogen-bonding pattern that was reconciled with the observed dehydration behaviour of PM. 

Model-free kinetic analysis of nonsteady-state reactions is a recent development that began with the thin zone microreactor configuration [82, 88, 89]. A model-free kinetic method known as the Y-procedure has been used to extract the nonsteady-state rate of chemical transformation from reaction-diffusion data with no assumptions regarding the kinetic model the reader is referred to [90] for more details describing this procedure. 

Rates of reaction of both these types of curing experiments are very useful to polymer scientists. There are several different kinetics software packages available to characterize materials. There are scanning kinetics, isothermal kinetics and model-free kinetics calculations. Each has its own unique application or is best suited for certain applications. Figure 6 depicts the thermal curve of an epoxy cure with a second curve superimposed representing the percent area as the reaction advances. 

Surender Rajendran, Mahendran Arunjunai, Thamaraichelvan A., Alam Sarfaraz, and Vijayakumar Chinnaswamy Thangavel. Curing studies of bisphenol A based bismaleimide and Cloisite 15A nanoclay blends using differential scanning calorimetry and model-free kinetics. J. Appl. Polym. Sci. 128 no. 1 (2013) 712-724. 

Vyazovkin (1997, 2001) developed an enhanced isoconversional method that allows evaluation of an effective activation energy ( ) as a function of the extent of reaction (a). This methodology, often referred to as model-free kinetics (MFK), is described in Section 3.5. The MFK software allows calculations such as conversion-time plots at selected temperatures that can be compared with actual measured data. It also allows the calculation of DSC curves that can be compared with actual measured DSC curves to help validate the analyses. The same curves analyzed by ASTM kinetics may be evaluated by MFK kinetics, and the same guidance is given. MFK kinetics is very comprehensive in that it is applicable to the simplest as well as to the most complex cure reactions, provided that a baseline can be drawn between a clear beginning and a clear end of the reaction. But it should be pointed out that the software is provided only by Mettler Toledo and Perkin-Elmer. For other users it is possible to measure versus conversion by the ASTM method and generate a spreadsheet with the appropriate MFK equation [e.g., Eq. (3.31) in Chapter 3], to calculate conversion-time plots. 

Model-free kinetics software employs numerical integration methods to measure activation energy versus conversion from cure exotherms at three or more heating rates, or from isothermal data at three or more temperatures. In both cases a minimum of four runs is recommended. Predictions like conversion-time plots and calculated DSC curves are made using Eq. (3.31). An advanced version of MFK software allows analysis of data from arbitrary heating programs, such as combined ramp and isothermal. A drawback of the commercial software is that a discrete mathematical relationship is not produced that can be exported and incorporated into cure models. 

Van Mele et al. (1995) describe a mobility factor that can be measured by MTDSC and approximates the diffusion factor in Eq. (2.90) see Section 2.13 on modulated temperature DSC. Kenny and Trivisano (1991) and Kenny et al. (1992) present a phenomenological approach to the shift from chemical control to diffusion-control of the cure reaction. Schawe (2002) also presents a phenomenological approach that uses model-free kinetics to evaluate the chemically controlled kinetics and introduces a diffusion-controlled function. 

Majehrzak, K.I., Nowak, W. Application of model-free kinetics to the study of dehydration of fly ash-based zeolites. Thermochim. Acta 413, 23-29 (2004)... 

From such conversion curves it is possible to obtain information about the reaction kinetics of the system observed using kinetic models or also with model-free kinetics (similar to with DSC). 

Model-free kinetic analysis of nonsteady-state reactions was recently introduced, allowing extraction of the nonsteady-state rate from reaction-diffusion data without assuming a particular kinetic model. Details about the so-called Y-procedure are reported by Yablonsky et al. [3]. 

Ramani, R. and Alam, S., Composition optimization of PEEK/PEI blend nsing model-free kinetics analysis, Thermochim. Acta, 511 (1-2), 179-188 (2010) DOl 10.1016/j.tca.2010.08.012. 

TGA provides general information about the overall reaction kinetics and is commonly used to estimate kinetic parameters. A model-free kinetic approach based on the isoconversional Friedmans method was used to analyze data obtained by TGA. The method gives simultaneously the activation energy and pre-exponential factor by assuming a reaction order without knowing the rate dependence on conversion. 

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